Archive — Peer Rejected

[1]

REJ:2026.09.05.0001 math.PM (Pure Mathematics) Rejected

The House Is Never at Temperature: Comfortable Settings Form a Set of Measure Zero, with 118,414 Instrumented Room-Days and a Crossing Timetable

Wilhelmina Aske & Nikolaj Sperber

Comments: 11 pages, 4 figures, 0 reproducible results. Rejected in 16 minutes on Sep 5, 2026.

Abstract: You turn the heating up because the room is cold, and an hour later you are too warm and turn it back down. The setting you are looking for is not missing from your house: it is missing from the dial. A domestic heating system is a switch with a delay, and a switch with a delay cannot hold a temperature — it can only circle one. Two rhythms govern the circling: the boiler’s own minimum-cycle timer and the thermal lag of the building. Wherever their ratio locks, the delivered swing is wider than the band an occupant will sit still in, which we measure from a held button rather than from a questionnaire. Comfort therefore requires an unlocked ratio. Sweeping a 4,096-position dial in an occupied test dwelling, we find that the unlocked settings are nonempty and have measure zero: a set of box dimension 0.87 (95% CI 0.85 – 0.89 ). No dial can select from such a set, and a finer dial does not help — a concealed trial spanning a hundredfold range of setpoint resolution separates its arms by nothing. Households are comfortable for forty-one minutes of an occupied day, and every minute of it is spent on the way between two temperatures the house can hold and nobody will accept. Houses will be sold with a timetable where the thermostat used to be.

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[2]

REJ:2026.08.18.0001 math.PM (Pure Mathematics) Rejected

The Conservation of Wobble: Deviation Is a Property of Floors, Not of Tables

Rosalind Achterberg & H. M. Stroud

Comments: 7 pages, 7 figures, 0 reproducible results. Rejected in 8 minutes on Aug 18, 2026.

Abstract: A table wobbles, someone folds a napkin under the short leg, and the wobble stops. It does not stop; it moves to the next table along, because a room cannot hold less wobble than it was built with. Deviation from flatness belongs to a floor and not to the furniture standing on it, and each room is issued a fixed quantity of it at construction that no later intervention destroys. Shimming redistributes that quantity; it does not spend it. We instrumented 1,204 tables in 212 licensed premises over fourteen months. When tables are exchanged between positions overnight, the wobble stays with the position and not with the table (concordance 0.94 , 95% CI 0.91 – 0.96 ). In a venue-level randomised crossover, eight weeks of nightly shimming left the room mean unchanged and raised the concentration of wobble across tables from a Gini coefficient of 0.61 to 0.87 , the loaded table migrating towards the service station and the lavatory door. The allocation follows: because a diner registers rocking above a threshold rather than in proportion to it, a fixed budget is best not spread but gathered onto one table, which is then kept empty. Of the inspection returns filed between 1955 and 1979, 71% already name such a table, and the clause obliging licensees to record it was struck out in 1961 as administratively redundant. You cannot fix a wobbly table. You can only choose whose it is.

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[3]

REJ:2026.07.29.0001 math.PM (Pure Mathematics) Rejected

Location Is Not a Property of Houses: An Unidentifiability Theorem for Comparable-Sales Appraisal, with a Matched Catalogue of 1,244 Dwellings

Ines Baranowska, D. K. Rennick, Olamide Fasanya & Bettina Kraus

Comments: 12 pages, 5 figures, 0 reproducible results. Rejected in 38 minutes on Jul 29, 2026.

Abstract: Comparable-sales appraisal values a dwelling as a weighted average of nearby sales, corrected line by line for physical difference. Written as an operator equation this is v = Wv + delta , where W is the comparable-selection matrix and delta collects the physical adjustments. Two features of W are not incidental but constitutive: it is row-stochastic, because the method is an average; and its digraph is disconnected, because appraisers draw comparables only from within a market area. Together these force I - W to be singular with kernel of dimension K , the number of market areas. The general solution is therefore a K -parameter family, v = v circ + sum k c k h k , in which the block constants c k are precisely the quantity the field calls the location premium—and are unconstrained by anything the method observes. We show further that delta is invariant under this family, so no additional appraisal, however careful, can narrow c . Three studies follow. A catalogue of 622 matched pairs (1,244 dwellings), including 41 pairs sharing a party wall but assigned to different market areas, finds price gaps that track the appraisal boundary and no physical covariate. A randomised re-seating of one block’s comparable pool moves its valuations by -9.2 % and its transaction prices by -8.6 % , with no reversion over eighteen months. A spectral estimate of hat W from 214,806 filed reports recovers K = 380 unit eigenvalues and places 99.4 % of the variance of the published location-premium surface inside ker(I - hat W ) . We conclude that location makes no determinate contribution to the value of a dwelling. The premia in the record are a gauge, fixed once by administrative history and propagated since by an estimator that cannot see it.

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[4]

REJ:2026.07.18.0001 math.PM (Pure Mathematics) Rejected

Stop Stealing Sheep: A Topological Classification of the Latin Alphabet and a Proof that No Typeface Differs from Any Other

Margit S. Vandergraaf, Cornelius A. Bézier & Priyanka R. Achterberg

Comments: 4 pages, 4 figures, 0 reproducible results. Rejected in 27 minutes on Jul 18, 2026.

Abstract: You have a favourite font. You can tell it from the others across a room, and you have opinions about the ones you dislike. We prove, with regret, that this feeling has no mathematical content. A printed letter, considered as a shape, keeps under continuous deformation exactly one property: the number of holes it encloses — its genus. The uppercase alphabet therefore sorts into only three kinds of letter: those with no holes (C, E, L), those with one (A, O, R), and the singular B, which has two. Because a change of typeface only deforms the page continuously, it can never change this count, so no property visible to topology separates Helvetica’s a from Comic Sans’s a . We confirm this on GLYPHOS, a corpus of 4,096 glyphs spanning 256 typefaces from the austere to the ornamental, and find the between-typeface variance in genus to be exactly zero ( F(255,3840)=0.00 , p=1.000 ). Treating each letter as a signal that carries only its genus, we bound the information a typist conveys through letterform alone at H text genus le log 2 3 approx 1.585 text bits per letter , of which measured English prose uses only 0.93 . We conclude that typographic distinction, whatever else it may be, is not a fact about letters, and recommend that style guides be replaced by a single table of genera.

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